The generator matrix

 1  1  1  1  1  1  1  1  X  X  1
 0  2  0 2X+2  0 2X  2  2 2X  0  0
 0  0  2 2X+2  0 2X+2 2X+2 2X 2X+2  2  0
 0  0  0 2X 2X 2X  0 2X  0  0  0

generates a code of length 11 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+21x^8+48x^9+9x^10+352x^11+10x^12+48x^13+22x^14+1x^18

The gray image is a code over GF(2) with n=88, k=9 and d=32.
This code was found by Heurico 1.16 in -1.01e-007 seconds.